Cost sharing in networks: some open questions

The fertile application of cooperative game techniques to cost sharing problems on networks has so far concentrated on the Stand Alone core test of fairness and/or stability, and ignored many combinatorial optimization problems where this core can be empty. I submit there is much room for an axiomatic discussion of fair division in the latter problems, where Stand Alone objections are not implementable. But the computational complexity of optimal solutions is still a very severe obstacle to this approach